Peel the sweet potatoes and pumpkin and cut into small pieces. Boil pumpkin and sweet potato separately until soft. Drain.
In a large, thick-walled saucepan, heat half of the butter, add onions, cook for about 4-5 minutes, until soft.
Put the fillets in a saucepan with onions, pour 300 grams of water, bring to a boil, reduce heat, cook the fish for about 10 minutes. Remove the fish from the pan, transfer to a plate, and let cool. Set aside the fish broth.
Disassemble the cooled fish into large pieces, remove bones and skin. Set fish aside.
Rub the sweet potatoes through a sieve, add the remaining butter, salt, and pepper puree to taste. Strain the fish broth and pour it back into a clean saucepan. Put sweet potato puree in the same pan and pour milk, bring to a boil over medium heat, cook sweet potato puree soup for 2-3 minutes.
Add pumpkin pieces, fish, basil, and cream to the sweet potato soup. Season with salt and pepper to taste, heat over medium heat, but do not bring to a boil. Serve the sweet potato puree soup in portioned bowls immediately.